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      PAT 1051 Pop Sequence (25)
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        <h2 id="题目要求">题目要求</h2><p>Given a stack which can keep M numbers at most. Push N numbers in the order of 1, 2, 3, …, N and pop randomly. You are supposed to tell if a given sequence of numbers is a possible pop sequence of the stack. For example, if M is 5 and N is 7, we can obtain 1, 2, 3, 4, 5, 6, 7 from the stack, but not 3, 2, 1, 7, 5, 6, 4.</p>
<a id="more"></a>
<h4 id="Input_Specification:">Input Specification:</h4><p>Each input file contains one test case. For each case, the first line contains 3 numbers (all no more than 1000): M (the maximum capacity of the stack), N (the length of push sequence), and K (the number of pop sequences to be checked). Then K lines follow, each contains a pop sequence of N numbers. All the numbers in a line are separated by a space.</p>
<h4 id="Output_Specification:">Output Specification:</h4><p>For each pop sequence, print in one line “YES” if it is indeed a possible pop sequence of the stack, or “NO” if not.</p>
<h4 id="Sample_Input:">Sample Input:</h4><figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><span class="line"><span class="number">5</span> <span class="number">7</span> <span class="number">5</span></span><br><span class="line"><span class="number">1</span> <span class="number">2</span> <span class="number">3</span> <span class="number">4</span> <span class="number">5</span> <span class="number">6</span> <span class="number">7</span></span><br><span class="line"><span class="number">3</span> <span class="number">2</span> <span class="number">1</span> <span class="number">7</span> <span class="number">5</span> <span class="number">6</span> <span class="number">4</span></span><br><span class="line"><span class="number">7</span> <span class="number">6</span> <span class="number">5</span> <span class="number">4</span> <span class="number">3</span> <span class="number">2</span> <span class="number">1</span></span><br><span class="line"><span class="number">5</span> <span class="number">6</span> <span class="number">4</span> <span class="number">3</span> <span class="number">7</span> <span class="number">2</span> <span class="number">1</span></span><br><span class="line"><span class="number">1</span> <span class="number">7</span> <span class="number">6</span> <span class="number">5</span> <span class="number">4</span> <span class="number">3</span> <span class="number">2</span></span><br></pre></td></tr></table></figure>
<h4 id="Sample_Output:">Sample Output:</h4><figure class="highlight gams"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">YES</span></span><br><span class="line"><span class="keyword">NO</span></span><br><span class="line"><span class="keyword">NO</span></span><br><span class="line"><span class="keyword">YES</span></span><br><span class="line"><span class="keyword">NO</span></span><br></pre></td></tr></table></figure>
<h2 id="解题思路">解题思路</h2><p>本题主要使用了STL中的栈（stack）来模拟一个栈进行操作。</p>
<p>使用cur记录当前应该入栈的元素，依次读取pop sequence中的元素，对于每个读取到的元素，主要遵循以下几个原则：</p>
<ol>
<li>如果要输出的元素正好是当前栈顶的元素，则栈顶出栈</li>
<li>如果要输出的元素大于等于cur，则将[cur, 要输出元素]这一区间内的元素全部入栈，然后出栈一次。出栈前判断栈是否溢出，如果溢出，则直接输出NO</li>
<li>如果要输出的元素小于cur，并且栈顶不是该元素（出栈得到的不是目的元素），则直接输出NO</li>
</ol>
<p>一个pop sequence里的元素全部读取处理完毕，并且没有出现错误，则输出YES。</p>
<h2 id="代码">代码</h2><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br></pre></td><td class="code"><pre><span class="line"><span class="preprocessor">#<span class="keyword">include</span> <span class="string">&lt;cstdio&gt;</span></span></span><br><span class="line"><span class="preprocessor">#<span class="keyword">include</span> <span class="string">&lt;cstdlib&gt;</span></span></span><br><span class="line"><span class="preprocessor">#<span class="keyword">include</span> <span class="string">&lt;stack&gt;</span></span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span><br><span class="line"></span>&#123;</span><br><span class="line">	<span class="keyword">int</span> num;</span><br><span class="line">	<span class="keyword">int</span> m, n, k;</span><br><span class="line">	<span class="built_in">scanf</span>(<span class="string">"%d%d%d"</span>, &amp;m, &amp;n, &amp;k);</span><br><span class="line">	<span class="keyword">bool</span> ok = <span class="literal">true</span>;</span><br><span class="line">	<span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">0</span>; i &lt; k; i++)</span><br><span class="line">	&#123;</span><br><span class="line">		<span class="built_in">stack</span>&lt;<span class="keyword">int</span>&gt; s;</span><br><span class="line">		<span class="keyword">int</span> cur = <span class="number">1</span>;</span><br><span class="line">		ok = <span class="literal">true</span>;</span><br><span class="line">		<span class="keyword">for</span> (<span class="keyword">int</span> j = <span class="number">0</span>; j &lt; n; j++)</span><br><span class="line">		&#123;</span><br><span class="line">			<span class="built_in">scanf</span>(<span class="string">"%d"</span>, &amp;num);</span><br><span class="line">			<span class="keyword">if</span> (!ok)</span><br><span class="line">			&#123;</span><br><span class="line">				<span class="keyword">continue</span>;</span><br><span class="line">			&#125;</span><br><span class="line">			<span class="keyword">if</span> (!s.empty() &amp;&amp; num == s.top())</span><br><span class="line">			&#123;</span><br><span class="line">				s.pop();</span><br><span class="line">			&#125;</span><br><span class="line">			<span class="keyword">else</span> <span class="keyword">if</span> (num &lt; cur &amp;&amp; num != s.top())</span><br><span class="line">			&#123;</span><br><span class="line">				<span class="built_in">printf</span>(<span class="string">"NO\n"</span>);</span><br><span class="line">				ok = <span class="literal">false</span>;</span><br><span class="line">			&#125;</span><br><span class="line">			<span class="keyword">else</span></span><br><span class="line">			&#123;</span><br><span class="line">				<span class="keyword">while</span> (cur &lt;= num)</span><br><span class="line">				&#123;</span><br><span class="line">					s.push(cur);</span><br><span class="line">					cur++;</span><br><span class="line">				&#125;</span><br><span class="line">				<span class="keyword">if</span> (s.size() &gt; m)</span><br><span class="line">				&#123;</span><br><span class="line">					<span class="built_in">printf</span>(<span class="string">"NO\n"</span>);</span><br><span class="line">					ok = <span class="literal">false</span>;</span><br><span class="line">				&#125;</span><br><span class="line">				s.pop();</span><br><span class="line">			&#125;</span><br><span class="line">		&#125;</span><br><span class="line">		<span class="keyword">if</span> (ok)</span><br><span class="line">		&#123;</span><br><span class="line">			<span class="built_in">printf</span>(<span class="string">"YES\n"</span>);</span><br><span class="line">		&#125;</span><br><span class="line">	&#125;</span><br><span class="line"></span><br><span class="line">	system(<span class="string">"pause"</span>);</span><br><span class="line">	<span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
      
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